12a
0635
(K12a
0635
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 11 2 1 5 12 6 4 8
Solving Sequence
2,7 3,10
4 1 8 6 11 5 12 9
c
2
c
3
c
1
c
7
c
6
c
10
c
5
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h−3.40397 × 10
99
u
123
+ 5.19308 × 10
98
u
122
+ ··· + 3.43279 × 10
98
b + 2.80609 × 10
100
,
− 2.32977 × 10
100
u
123
+ 3.31992 × 10
99
u
122
+ ··· + 2.40295 × 10
99
a + 1.54517 × 10
101
,
u
124
− u
123
+ ··· − 10u + 7i
I
u
2
= h−2u
23
− 3u
22
+ ··· + b + 3, −2u
23
− 4u
22
+ ··· + a + 4, u
24
− 7u
22
+ ··· − 3u
2
+ 1i
* 2 irreducible components of dim
C
= 0, with total 148 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h−3.40 × 10
99
u
123
+ 5.19 × 10
98
u
122
+ · · · + 3.43 × 10
98
b + 2.81 ×
10
100
, −2.33 × 10
100
u
123
+ 3.32 × 10
99
u
122
+ · · · + 2.40 × 10
99
a + 1.55 ×
10
101
, u
124
− u
123
+ · · · − 10u + 7i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
9.69545u
123
− 1.38160u
122
+ ··· + 17.6957u − 64.3030
9.91607u
123
− 1.51279u
122
+ ··· + 21.3533u − 81.7439
a
4
=
−1.32214u
123
− 1.03175u
122
+ ··· − 10.3796u + 21.7586
−4.74984u
123
− 1.01744u
122
+ ··· − 28.6100u + 51.0642
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
7.83332u
123
− 1.40369u
122
+ ··· + 17.0457u − 64.9290
8.05394u
123
− 1.53487u
122
+ ··· + 20.7033u − 82.3699
a
5
=
−6.00946u
123
+ 0.590204u
122
+ ··· − 16.6985u + 37.3812
−0.870989u
123
+ 0.301695u
122
+ ··· + 0.280302u + 4.54417
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
a
9
=
7.27947u
123
− 1.24156u
122
+ ··· + 12.2294u − 56.5649
9.78691u
123
− 1.89303u
122
+ ··· + 22.0872u − 94.9113
(ii) Obstruction class = −1
(iii) Cusp Shapes = −25.9880u
123
+ 7.91471u
122
+ ··· − 61.1217u + 214.607
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
124
+ 69u
123
+ ··· + 324u + 49
c
2
, c
6
u
124
− u
123
+ ··· − 10u + 7
c
3
u
124
+ 21u
122
+ ··· + 39652872u + 5579953
c
4
, c
8
u
124
+ 2u
123
+ ··· + 1136u + 751
c
5
, c
10
u
124
+ u
123
+ ··· − 3985u + 173
c
7
, c
12
u
124
− 3u
123
+ ··· − 14693u + 4312
c
9
u
124
+ 19u
123
+ ··· + 33u + 1
c
11
u
124
− 3u
123
+ ··· − 9u + 2
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
124
− 21y
123
+ ··· − 81456y + 2401
c
2
, c
6
y
124
− 69y
123
+ ··· − 324y + 49
c
3
y
124
+ 42y
123
+ ··· + 1234397237289356y + 31135875482209
c
4
, c
8
y
124
+ 70y
123
+ ··· + 4643906y + 564001
c
5
, c
10
y
124
+ 97y
123
+ ··· − 5851069y + 29929
c
7
, c
12
y
124
+ 111y
123
+ ··· − 621048393y + 18593344
c
9
y
124
− 3y
123
+ ··· + 405y + 1
c
11
y
124
− y
123
+ ··· + 71y + 4
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889763 + 0.507744I
a = −1.78676 + 1.06679I
b = −0.76579 + 1.44957I
3.58375 + 6.97795I 0
u = −0.889763 − 0.507744I
a = −1.78676 − 1.06679I
b = −0.76579 − 1.44957I
3.58375 − 6.97795I 0
u = 0.945691 + 0.402211I
a = −1.29680 − 1.16543I
b = −0.89408 − 1.38943I
−0.16775 − 3.71028I 0
u = 0.945691 − 0.402211I
a = −1.29680 + 1.16543I
b = −0.89408 + 1.38943I
−0.16775 + 3.71028I 0
u = −0.876377 + 0.394634I
a = −1.93332 − 1.22206I
b = −2.20005 + 0.10005I
−2.76946 + 2.00721I 0
u = −0.876377 − 0.394634I
a = −1.93332 + 1.22206I
b = −2.20005 − 0.10005I
−2.76946 − 2.00721I 0
u = 1.002310 + 0.295642I
a = −0.82558 − 1.43356I
b = −0.89433 − 1.44500I
0.02006 − 3.75240I 0
u = 1.002310 − 0.295642I
a = −0.82558 + 1.43356I
b = −0.89433 + 1.44500I
0.02006 + 3.75240I 0
u = −0.823156 + 0.666752I
a = −0.746673 − 1.090280I
b = −1.47353 − 0.15266I
−1.72676 + 2.56150I 0
u = −0.823156 − 0.666752I
a = −0.746673 + 1.090280I
b = −1.47353 + 0.15266I
−1.72676 − 2.56150I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.853822 + 0.394425I
a = 1.21120 − 1.31062I
b = 1.31262 − 2.44704I
1.29001 + 5.01865I 0
u = −0.853822 − 0.394425I
a = 1.21120 + 1.31062I
b = 1.31262 + 2.44704I
1.29001 − 5.01865I 0
u = 0.768921 + 0.534067I
a = 0.46891 − 1.34274I
b = 0.921603 − 1.020550I
2.71627 − 2.21713I 0
u = 0.768921 − 0.534067I
a = 0.46891 + 1.34274I
b = 0.921603 + 1.020550I
2.71627 + 2.21713I 0
u = 0.996957 + 0.392353I
a = −2.20990 − 0.25684I
b = −1.85601 − 1.40774I
−1.51548 − 5.69067I 0
u = 0.996957 − 0.392353I
a = −2.20990 + 0.25684I
b = −1.85601 + 1.40774I
−1.51548 + 5.69067I 0
u = 0.764261 + 0.525513I
a = 1.33835 − 0.92085I
b = 1.383260 − 0.265113I
2.72829 − 2.08959I 0
u = 0.764261 − 0.525513I
a = 1.33835 + 0.92085I
b = 1.383260 + 0.265113I
2.72829 + 2.08959I 0
u = −1.044810 + 0.245038I
a = 0.019646 − 0.869080I
b = −0.552022 + 0.084685I
−2.52525 + 0.11799I 0
u = −1.044810 − 0.245038I
a = 0.019646 + 0.869080I
b = −0.552022 − 0.084685I
−2.52525 − 0.11799I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.942798 + 0.518681I
a = 2.26119 + 0.22869I
b = 2.51625 − 0.87136I
−3.45548 + 6.95335I 0
u = −0.942798 − 0.518681I
a = 2.26119 − 0.22869I
b = 2.51625 + 0.87136I
−3.45548 − 6.95335I 0
u = 0.550493 + 0.735340I
a = −0.376700 + 1.173790I
b = −1.152420 + 0.198373I
1.38554 − 5.06519I 0
u = 0.550493 − 0.735340I
a = −0.376700 − 1.173790I
b = −1.152420 − 0.198373I
1.38554 + 5.06519I 0
u = −0.890883 + 0.191319I
a = 0.580557 − 0.563384I
b = 0.052645 − 0.231219I
−1.53140 + 0.64514I 0
u = −0.890883 − 0.191319I
a = 0.580557 + 0.563384I
b = 0.052645 + 0.231219I
−1.53140 − 0.64514I 0
u = 0.084174 + 0.906109I
a = −0.931218 − 0.602335I
b = 0.300318 − 0.615097I
−5.86891 + 0.84019I 0
u = 0.084174 − 0.906109I
a = −0.931218 + 0.602335I
b = 0.300318 + 0.615097I
−5.86891 − 0.84019I 0
u = 1.089000 + 0.057770I
a = −0.458899 − 0.176996I
b = −0.241678 + 1.036480I
−6.73622 + 1.56313I 0
u = 1.089000 − 0.057770I
a = −0.458899 + 0.176996I
b = −0.241678 − 1.036480I
−6.73622 − 1.56313I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.841789 + 0.308490I
a = −0.253112 + 1.389370I
b = −1.010470 − 0.355714I
−3.35843 − 1.40319I 0
u = 0.841789 − 0.308490I
a = −0.253112 − 1.389370I
b = −1.010470 + 0.355714I
−3.35843 + 1.40319I 0
u = 0.850162 + 0.258786I
a = 2.34668 + 0.80322I
b = 2.63478 + 1.53622I
0.42242 + 1.57962I 0
u = 0.850162 − 0.258786I
a = 2.34668 − 0.80322I
b = 2.63478 − 1.53622I
0.42242 − 1.57962I 0
u = −0.165198 + 0.869947I
a = −1.108970 + 0.817177I
b = 0.461300 + 0.688223I
−5.64795 − 4.21433I 0
u = −0.165198 − 0.869947I
a = −1.108970 − 0.817177I
b = 0.461300 − 0.688223I
−5.64795 + 4.21433I 0
u = 0.129719 + 0.875650I
a = 1.39433 + 0.79952I
b = −0.315673 + 1.197660I
−4.74076 + 13.31180I 0
u = 0.129719 − 0.875650I
a = 1.39433 − 0.79952I
b = −0.315673 − 1.197660I
−4.74076 − 13.31180I 0
u = 0.535374 + 0.702510I
a = −0.70273 − 1.60720I
b = 0.701838 − 1.188810I
1.33621 + 7.70254I 0
u = 0.535374 − 0.702510I
a = −0.70273 + 1.60720I
b = 0.701838 + 1.188810I
1.33621 − 7.70254I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.963671 + 0.596228I
a = 1.93246 − 0.19022I
b = 2.12635 + 1.00542I
0.09405 − 12.64730I 0
u = 0.963671 − 0.596228I
a = 1.93246 + 0.19022I
b = 2.12635 − 1.00542I
0.09405 + 12.64730I 0
u = 0.031930 + 0.850171I
a = −1.286950 − 0.064024I
b = 0.384153 − 0.920669I
−5.65063 + 3.67795I 0. − 8.17604I
u = 0.031930 − 0.850171I
a = −1.286950 + 0.064024I
b = 0.384153 + 0.920669I
−5.65063 − 3.67795I 0. + 8.17604I
u = −0.101551 + 0.843765I
a = 1.38878 − 0.94054I
b = −0.214087 − 1.273220I
−7.69510 − 6.75726I 0. + 5.03105I
u = −0.101551 − 0.843765I
a = 1.38878 + 0.94054I
b = −0.214087 + 1.273220I
−7.69510 + 6.75726I 0. − 5.03105I
u = 0.837971 + 0.022047I
a = 1.64447 + 1.84336I
b = 0.67436 + 1.28251I
0.40219 + 3.27217I −1.49425 − 6.49968I
u = 0.837971 − 0.022047I
a = 1.64447 − 1.84336I
b = 0.67436 − 1.28251I
0.40219 − 3.27217I −1.49425 + 6.49968I
u = −1.057650 + 0.510566I
a = −0.398012 + 0.969133I
b = −0.25035 + 1.59862I
1.56493 + 2.71643I 0
u = −1.057650 − 0.510566I
a = −0.398012 − 0.969133I
b = −0.25035 − 1.59862I
1.56493 − 2.71643I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.989273 + 0.641767I
a = −0.793131 + 0.839980I
b = −1.43009 + 0.17053I
0.123254 − 0.138656I 0
u = 0.989273 − 0.641767I
a = −0.793131 − 0.839980I
b = −1.43009 − 0.17053I
0.123254 + 0.138656I 0
u = −0.094510 + 0.807577I
a = −0.464865 − 0.390483I
b = −0.196403 + 1.239820I
0.06766 − 6.76111I 2.52940 + 6.55266I
u = −0.094510 − 0.807577I
a = −0.464865 + 0.390483I
b = −0.196403 − 1.239820I
0.06766 + 6.76111I 2.52940 − 6.55266I
u = −0.730434 + 0.350457I
a = −2.29314 + 1.56310I
b = −1.23330 + 0.78842I
1.69870 − 1.66163I 7.41455 − 1.08859I
u = −0.730434 − 0.350457I
a = −2.29314 − 1.56310I
b = −1.23330 − 0.78842I
1.69870 + 1.66163I 7.41455 + 1.08859I
u = −1.194320 + 0.015055I
a = −0.190612 − 0.231367I
b = 0.047022 + 0.853370I
−4.49045 + 6.47677I 0
u = −1.194320 − 0.015055I
a = −0.190612 + 0.231367I
b = 0.047022 − 0.853370I
−4.49045 − 6.47677I 0
u = 0.030886 + 0.803159I
a = −0.381768 + 0.007558I
b = −0.222971 − 0.985008I
−3.41325 + 2.13889I −0.30087 − 3.11100I
u = 0.030886 − 0.803159I
a = −0.381768 − 0.007558I
b = −0.222971 + 0.985008I
−3.41325 − 2.13889I −0.30087 + 3.11100I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.603352 + 0.525352I
a = 1.34188 − 0.48358I
b = 0.68124 − 1.48669I
4.39388 − 2.75837I 8.32431 + 1.65329I
u = −0.603352 − 0.525352I
a = 1.34188 + 0.48358I
b = 0.68124 + 1.48669I
4.39388 + 2.75837I 8.32431 − 1.65329I
u = −1.152550 + 0.380660I
a = −0.029035 − 0.952780I
b = −0.172822 − 0.501079I
−3.38514 + 0.72503I 0
u = −1.152550 − 0.380660I
a = −0.029035 + 0.952780I
b = −0.172822 + 0.501079I
−3.38514 − 0.72503I 0
u = −0.015556 + 0.785715I
a = −1.66867 + 0.26406I
b = 0.448769 + 0.777216I
−5.42277 − 0.55359I −0.973571 − 0.814051I
u = −0.015556 − 0.785715I
a = −1.66867 − 0.26406I
b = 0.448769 − 0.777216I
−5.42277 + 0.55359I −0.973571 + 0.814051I
u = −0.032020 + 0.781364I
a = 2.14449 + 0.28280I
b = 0.732638 + 0.220976I
−1.35725 − 3.79869I 1.65172 + 4.10455I
u = −0.032020 − 0.781364I
a = 2.14449 − 0.28280I
b = 0.732638 − 0.220976I
−1.35725 + 3.79869I 1.65172 − 4.10455I
u = 0.170088 + 0.730003I
a = −0.071230 + 0.676753I
b = −0.731808 + 0.468895I
0.37028 + 2.87213I 1.28510 + 0.62817I
u = 0.170088 − 0.730003I
a = −0.071230 − 0.676753I
b = −0.731808 − 0.468895I
0.37028 − 2.87213I 1.28510 − 0.62817I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.172590 + 0.435603I
a = 0.81891 − 1.24137I
b = 0.062991 − 0.825371I
−2.73012 + 1.51532I 0
u = −1.172590 − 0.435603I
a = 0.81891 + 1.24137I
b = 0.062991 + 0.825371I
−2.73012 − 1.51532I 0
u = −0.488087 + 0.554663I
a = −0.85842 + 2.10605I
b = 0.504340 + 1.307040I
−2.20840 − 2.63961I 0.25032 + 3.28418I
u = −0.488087 − 0.554663I
a = −0.85842 − 2.10605I
b = 0.504340 − 1.307040I
−2.20840 + 2.63961I 0.25032 − 3.28418I
u = 1.173020 + 0.480755I
a = −1.84719 − 0.48053I
b = −1.54303 − 1.18598I
−2.39613 − 6.88242I 0
u = 1.173020 − 0.480755I
a = −1.84719 + 0.48053I
b = −1.54303 + 1.18598I
−2.39613 + 6.88242I 0
u = 1.164020 + 0.504706I
a = −1.117050 + 0.657690I
b = −1.277680 + 0.300223I
−2.50842 − 7.51034I 0
u = 1.164020 − 0.504706I
a = −1.117050 − 0.657690I
b = −1.277680 − 0.300223I
−2.50842 + 7.51034I 0
u = −0.562348 + 0.453906I
a = −0.33839 − 1.87897I
b = −1.31334 − 0.66272I
−1.96835 + 1.60122I −0.51057 − 4.13265I
u = −0.562348 − 0.453906I
a = −0.33839 + 1.87897I
b = −1.31334 + 0.66272I
−1.96835 − 1.60122I −0.51057 + 4.13265I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.216150 + 0.409530I
a = −0.809824 − 0.995513I
b = 0.236122 − 1.216550I
−3.82762 + 2.56614I 0
u = 1.216150 − 0.409530I
a = −0.809824 + 0.995513I
b = 0.236122 + 1.216550I
−3.82762 − 2.56614I 0
u = 1.206620 + 0.442321I
a = −0.65156 − 1.85727I
b = −0.96275 − 2.66504I
−4.96595 − 0.54583I 0
u = 1.206620 − 0.442321I
a = −0.65156 + 1.85727I
b = −0.96275 + 2.66504I
−4.96595 + 0.54583I 0
u = 1.208230 + 0.450329I
a = 0.143311 − 0.112206I
b = 0.931908 + 1.029250I
−8.99309 − 3.85792I 0
u = 1.208230 − 0.450329I
a = 0.143311 + 0.112206I
b = 0.931908 − 1.029250I
−8.99309 + 3.85792I 0
u = −1.203870 + 0.469104I
a = 0.09329 + 1.65147I
b = −0.15745 + 2.52338I
−4.77346 + 8.32914I 0
u = −1.203870 − 0.469104I
a = 0.09329 − 1.65147I
b = −0.15745 − 2.52338I
−4.77346 − 8.32914I 0
u = −1.207550 + 0.462777I
a = 1.74836 − 0.92839I
b = 1.83396 − 2.26101I
−8.90383 + 5.05532I 0
u = −1.207550 − 0.462777I
a = 1.74836 + 0.92839I
b = 1.83396 + 2.26101I
−8.90383 − 5.05532I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.215380 + 0.442634I
a = −0.904898 + 0.542762I
b = −0.235963 + 0.654580I
−7.08584 + 2.27065I 0
u = −1.215380 − 0.442634I
a = −0.904898 − 0.542762I
b = −0.235963 − 0.654580I
−7.08584 − 2.27065I 0
u = 1.212780 + 0.469577I
a = 0.90744 + 1.19643I
b = 0.30638 + 1.45771I
−6.89339 − 6.73073I 0
u = 1.212780 − 0.469577I
a = 0.90744 − 1.19643I
b = 0.30638 − 1.45771I
−6.89339 + 6.73073I 0
u = 1.250340 + 0.358838I
a = −0.154675 + 0.085690I
b = 0.222334 + 1.125380I
−10.06870 + 0.09249I 0
u = 1.250340 − 0.358838I
a = −0.154675 − 0.085690I
b = 0.222334 − 1.125380I
−10.06870 − 0.09249I 0
u = 1.239790 + 0.401403I
a = 0.837353 + 0.127179I
b = 0.201578 − 0.766582I
−11.77270 + 2.46110I 0
u = 1.239790 − 0.401403I
a = 0.837353 − 0.127179I
b = 0.201578 + 0.766582I
−11.77270 − 2.46110I 0
u = −1.205740 + 0.496070I
a = 0.98021 − 1.36199I
b = −0.01005 − 1.80166I
−3.21033 + 11.52210I 0
u = −1.205740 − 0.496070I
a = 0.98021 + 1.36199I
b = −0.01005 + 1.80166I
−3.21033 − 11.52210I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.346470 + 0.598546I
a = 1.56949 + 0.18723I
b = 0.643607 − 0.281030I
3.57068 + 1.66346I 7.95681 − 0.97959I
u = −0.346470 − 0.598546I
a = 1.56949 − 0.18723I
b = 0.643607 + 0.281030I
3.57068 − 1.66346I 7.95681 + 0.97959I
u = −1.261730 + 0.381247I
a = 0.550601 − 0.130699I
b = −0.158238 + 0.822053I
−9.06425 − 9.00214I 0
u = −1.261730 − 0.381247I
a = 0.550601 + 0.130699I
b = −0.158238 − 0.822053I
−9.06425 + 9.00214I 0
u = −1.217400 + 0.506078I
a = −2.07512 + 1.15288I
b = −2.12363 + 2.21754I
−11.0212 + 11.6591I 0
u = −1.217400 − 0.506078I
a = −2.07512 − 1.15288I
b = −2.12363 − 2.21754I
−11.0212 − 11.6591I 0
u = −1.241340 + 0.444472I
a = −0.016637 + 0.324766I
b = 0.887868 − 0.518383I
−9.48502 + 0.89689I 0
u = −1.241340 − 0.444472I
a = −0.016637 − 0.324766I
b = 0.887868 + 0.518383I
−9.48502 − 0.89689I 0
u = 0.097616 + 0.674455I
a = 0.713694 + 0.416425I
b = −0.503777 + 1.132830I
0.65401 + 2.46549I 5.02445 − 1.80014I
u = 0.097616 − 0.674455I
a = 0.713694 − 0.416425I
b = −0.503777 − 1.132830I
0.65401 − 2.46549I 5.02445 + 1.80014I
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.233200 + 0.477241I
a = 1.51555 + 1.07618I
b = 1.31004 + 2.29998I
−9.24636 − 8.43893I 0
u = 1.233200 − 0.477241I
a = 1.51555 − 1.07618I
b = 1.31004 − 2.29998I
−9.24636 + 8.43893I 0
u = −1.215910 + 0.536328I
a = 1.46121 − 0.53131I
b = 1.75921 − 1.56137I
−8.80606 + 9.34534I 0
u = −1.215910 − 0.536328I
a = 1.46121 + 0.53131I
b = 1.75921 + 1.56137I
−8.80606 − 9.34534I 0
u = 1.224110 + 0.524751I
a = −1.92450 − 1.07444I
b = −1.94585 − 2.26335I
−8.0296 − 18.3915I 0
u = 1.224110 − 0.524751I
a = −1.92450 + 1.07444I
b = −1.94585 + 2.26335I
−8.0296 + 18.3915I 0
u = −1.277340 + 0.411628I
a = −0.258038 − 0.020094I
b = 0.084685 − 0.846740I
−10.11280 + 3.75612I 0
u = −1.277340 − 0.411628I
a = −0.258038 + 0.020094I
b = 0.084685 + 0.846740I
−10.11280 − 3.75612I 0
u = 1.248000 + 0.508745I
a = 1.25587 + 0.67417I
b = 1.43654 + 1.48601I
−9.40797 − 5.92605I 0
u = 1.248000 − 0.508745I
a = 1.25587 − 0.67417I
b = 1.43654 − 1.48601I
−9.40797 + 5.92605I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.455083 + 0.372696I
a = 1.44631 + 0.18307I
b = 0.768449 + 0.641571I
1.164220 + 0.197770I 8.79841 − 0.47962I
u = 0.455083 − 0.372696I
a = 1.44631 − 0.18307I
b = 0.768449 − 0.641571I
1.164220 − 0.197770I 8.79841 + 0.47962I
u = 0.072835 + 0.491611I
a = 1.335550 + 0.017512I
b = −0.529551 + 0.952438I
0.66958 + 2.38733I 2.94044 − 2.16417I
u = 0.072835 − 0.491611I
a = 1.335550 − 0.017512I
b = −0.529551 − 0.952438I
0.66958 − 2.38733I 2.94044 + 2.16417I
17
II. I
u
2
=
h−2u
23
−3u
22
+· · ·+b+3, −2u
23
−4u
22
+· · ·+a+4, u
24
−7u
22
+· · ·−3u
2
+1i
(i) Arc colorings
a
2
=
1
0
a
7
=
0
u
a
3
=
1
u
2
a
10
=
2u
23
+ 4u
22
+ ··· + 12u
2
− 4
2u
23
+ 3u
22
+ ··· + 8u
2
− 3
a
4
=
−2u
23
− u
22
+ ··· − u + 1
−u
22
+ 6u
20
+ ··· − 2u
2
− 2u
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
3
+ u
u
7
− u
5
+ u
a
6
=
u
u
a
11
=
2u
23
+ 3u
22
+ ··· + 10u
2
− 3
2u
23
+ 2u
22
+ ··· + 6u
2
− 2
a
5
=
−2u
23
− 2u
22
+ ··· + 6u + 4
u
23
− 2u
22
+ ··· + 2u + 4
a
12
=
−u
8
+ 3u
6
− 3u
4
+ 1
−u
10
+ 2u
8
− u
6
− 2u
4
+ u
2
a
9
=
2u
23
+ 3u
22
+ ··· + 10u
2
− 4
2u
23
+ 2u
22
+ ··· + 6u
2
− 3
(ii) Obstruction class = 1
(iii) Cusp Shapes
= −17u
23
−u
22
+112u
21
+6u
20
−355u
19
−17u
18
+649u
17
+26u
16
−700u
15
−19u
14
+333u
13
−
3u
12
+ 164u
11
+ 33u
10
−370u
9
−68u
8
+ 212u
7
+ 81u
6
+ 2u
5
−43u
4
−60u
3
−3u
2
+ 26u + 5
18
(iv) u-Polynomials at the component
19
Crossings u-Polynomials at each crossing
c
1
u
24
− 14u
23
+ ··· − 6u + 1
c
2
u
24
− 7u
22
+ ··· − 3u
2
+ 1
c
3
u
24
+ u
23
+ ··· + 2u + 1
c
4
u
24
+ u
23
+ ··· + 12u
2
+ 1
c
5
u
24
+ 12u
22
+ ··· − u + 1
c
6
u
24
− 7u
22
+ ··· − 3u
2
+ 1
c
7
u
24
+ 9u
22
+ ··· − 3u
2
+ 1
c
8
u
24
− u
23
+ ··· + 12u
2
+ 1
c
9
u
24
− 2u
22
+ ··· + 7u + 1
c
10
u
24
+ 12u
22
+ ··· + u + 1
c
11
u
24
− 2u
23
+ ··· − u + 1
c
12
u
24
+ 9u
22
+ ··· − 3u
2
+ 1
20
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
24
− 2y
23
+ ··· − 10y + 1
c
2
, c
6
y
24
− 14y
23
+ ··· − 6y + 1
c
3
y
24
− 7y
23
+ ··· + 2y + 1
c
4
, c
8
y
24
+ 17y
23
+ ··· + 24y + 1
c
5
, c
10
y
24
+ 24y
23
+ ··· + 17y + 1
c
7
, c
12
y
24
+ 18y
23
+ ··· − 6y + 1
c
9
y
24
− 4y
23
+ ··· − 9y + 1
c
11
y
24
+ 2y
23
+ ··· − 7y + 1
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.830087 + 0.607865I
a = −0.787937 + 1.127550I
b = −1.48311 + 0.08212I
−1.31891 − 2.39167I 8.22171 + 0.99991I
u = 0.830087 − 0.607865I
a = −0.787937 − 1.127550I
b = −1.48311 − 0.08212I
−1.31891 + 2.39167I 8.22171 − 0.99991I
u = 0.999057 + 0.347047I
a = −1.36381 − 1.43525I
b = −1.19874 − 2.31003I
−0.26640 − 4.90016I −0.41787 + 8.67235I
u = 0.999057 − 0.347047I
a = −1.36381 + 1.43525I
b = −1.19874 + 2.31003I
−0.26640 + 4.90016I −0.41787 − 8.67235I
u = −0.898344 + 0.216416I
a = −0.84851 − 1.49922I
b = −1.331090 + 0.161552I
−3.88873 + 0.99670I −9.19138 + 1.06418I
u = −0.898344 − 0.216416I
a = −0.84851 + 1.49922I
b = −1.331090 − 0.161552I
−3.88873 − 0.99670I −9.19138 − 1.06418I
u = −0.974569 + 0.527157I
a = −0.756267 − 0.173046I
b = −1.314500 + 0.356894I
0.995615 + 0.733801I 3.68845 − 1.75573I
u = −0.974569 − 0.527157I
a = −0.756267 + 0.173046I
b = −1.314500 − 0.356894I
0.995615 − 0.733801I 3.68845 + 1.75573I
u = 0.070130 + 0.855176I
a = −1.284100 − 0.323500I
b = 0.379137 − 0.657760I
−5.48258 + 2.65917I 0.432647 − 0.716337I
u = 0.070130 − 0.855176I
a = −1.284100 + 0.323500I
b = 0.379137 + 0.657760I
−5.48258 − 2.65917I 0.432647 + 0.716337I
23
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.612663 + 0.473761I
a = 0.04247 − 1.73742I
b = −0.225243 − 0.783401I
2.10127 + 3.44984I 5.50500 − 5.25186I
u = −0.612663 − 0.473761I
a = 0.04247 + 1.73742I
b = −0.225243 + 0.783401I
2.10127 − 3.44984I 5.50500 + 5.25186I
u = 1.161630 + 0.417142I
a = −0.04559 − 1.76635I
b = 0.40212 − 1.45647I
−2.75004 − 0.15086I 2.66319 − 3.71566I
u = 1.161630 − 0.417142I
a = −0.04559 + 1.76635I
b = 0.40212 + 1.45647I
−2.75004 + 0.15086I 2.66319 + 3.71566I
u = −1.160360 + 0.486741I
a = 1.23692 + 0.81611I
b = 1.167500 + 0.316108I
−2.24622 + 8.08592I 2.57244 − 12.50899I
u = −1.160360 − 0.486741I
a = 1.23692 − 0.81611I
b = 1.167500 − 0.316108I
−2.24622 − 8.08592I 2.57244 + 12.50899I
u = 0.707470 + 0.179898I
a = 2.73022 + 2.10461I
b = 1.88663 + 1.35622I
0.97241 + 2.30300I 3.64056 − 4.71970I
u = 0.707470 − 0.179898I
a = 2.73022 − 2.10461I
b = 1.88663 − 1.35622I
0.97241 − 2.30300I 3.64056 + 4.71970I
u = −1.241630 + 0.425857I
a = 0.1166810 + 0.0396087I
b = 0.777120 − 0.932683I
−9.45240 + 1.79763I −3.66132 − 2.97351I
u = −1.241630 − 0.425857I
a = 0.1166810 − 0.0396087I
b = 0.777120 + 0.932683I
−9.45240 − 1.79763I −3.66132 + 2.97351I
24
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.112951 + 0.674509I
a = 0.137859 + 0.205443I
b = 1.066660 + 0.565024I
0.69686 − 3.66859I 5.64131 + 7.83145I
u = −0.112951 − 0.674509I
a = 0.137859 − 0.205443I
b = 1.066660 − 0.565024I
0.69686 + 3.66859I 5.64131 − 7.83145I
u = 1.232150 + 0.493085I
a = 1.32207 + 0.83590I
b = 1.37352 + 1.93665I
−8.96968 − 7.53432I −2.09474 + 3.83158I
u = 1.232150 − 0.493085I
a = 1.32207 − 0.83590I
b = 1.37352 − 1.93665I
−8.96968 + 7.53432I −2.09474 − 3.83158I
25
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
24
− 14u
23
+ ··· − 6u + 1)(u
124
+ 69u
123
+ ··· + 324u + 49)
c
2
(u
24
− 7u
22
+ ··· − 3u
2
+ 1)(u
124
− u
123
+ ··· − 10u + 7)
c
3
(u
24
+ u
23
+ ··· + 2u + 1)
· (u
124
+ 21u
122
+ ··· + 39652872u + 5579953)
c
4
(u
24
+ u
23
+ ··· + 12u
2
+ 1)(u
124
+ 2u
123
+ ··· + 1136u + 751)
c
5
(u
24
+ 12u
22
+ ··· − u + 1)(u
124
+ u
123
+ ··· − 3985u + 173)
c
6
(u
24
− 7u
22
+ ··· − 3u
2
+ 1)(u
124
− u
123
+ ··· − 10u + 7)
c
7
(u
24
+ 9u
22
+ ··· − 3u
2
+ 1)(u
124
− 3u
123
+ ··· − 14693u + 4312)
c
8
(u
24
− u
23
+ ··· + 12u
2
+ 1)(u
124
+ 2u
123
+ ··· + 1136u + 751)
c
9
(u
24
− 2u
22
+ ··· + 7u + 1)(u
124
+ 19u
123
+ ··· + 33u + 1)
c
10
(u
24
+ 12u
22
+ ··· + u + 1)(u
124
+ u
123
+ ··· − 3985u + 173)
c
11
(u
24
− 2u
23
+ ··· − u + 1)(u
124
− 3u
123
+ ··· − 9u + 2)
c
12
(u
24
+ 9u
22
+ ··· − 3u
2
+ 1)(u
124
− 3u
123
+ ··· − 14693u + 4312)
26
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
24
− 2y
23
+ ··· − 10y + 1)(y
124
− 21y
123
+ ··· − 81456y + 2401)
c
2
, c
6
(y
24
− 14y
23
+ ··· − 6y + 1)(y
124
− 69y
123
+ ··· − 324y + 49)
c
3
(y
24
− 7y
23
+ ··· + 2y + 1)
· (y
124
+ 42y
123
+ ··· + 1234397237289356y + 31135875482209)
c
4
, c
8
(y
24
+ 17y
23
+ ··· + 24y + 1)
· (y
124
+ 70y
123
+ ··· + 4643906y + 564001)
c
5
, c
10
(y
24
+ 24y
23
+ ··· + 17y + 1)
· (y
124
+ 97y
123
+ ··· − 5851069y + 29929)
c
7
, c
12
(y
24
+ 18y
23
+ ··· − 6y + 1)
· (y
124
+ 111y
123
+ ··· − 621048393y + 18593344)
c
9
(y
24
− 4y
23
+ ··· − 9y + 1)(y
124
− 3y
123
+ ··· + 405y + 1)
c
11
(y
24
+ 2y
23
+ ··· − 7y + 1)(y
124
− y
123
+ ··· + 71y + 4)
27
